Optimality of Walrand-Varaiya type policies and approximation results for zero delay coding of Markov sources

Wood, Richard; Linder, Tamás; Yüksel, Serdar

doi:10.1109/isit.2015.7282682

Cited by 4 publications

(3 citation statements)

References 28 publications

(7 reference statements)

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“…The first two terms in (20) match the first two terms in (14). The O 1 (log n) term is the penalty due to the shape of lattice quantizer cells not being exactly spherical, i.e.…”

Section: A Fully Observed Systemmentioning

confidence: 94%

“…Theorem 2 implies that if the channel F i → G i is noiseless, then there exists a quantizer with output entropy given by the right side of (20) that attains LQR cost b > tr(Σ V S)), when coupled with an appropriate controller. In fact, the bound in (20) is attainable by a simple lattice quantization scheme that only transmits the innovation of the state (a DPCM scheme). The controller computes the control action based on the quantized data as if it was the true state (the so-called certainty equivalence control).…”

Section: A Fully Observed Systemmentioning

confidence: 99%

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Rate-cost tradeoffs in control

Kostina

Hassibi

2016

2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate r bits/sec and the expected cost b. We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lowerbound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. [2]. The bound applies as long as the system noise has a probability density function. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variable-length vector quantization to prove that the new converse bounds are tight.

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“…The first two terms in (20) match the first two terms in (14). The O 1 (log n) term is the penalty due to the shape of lattice quantizer cells not being exactly spherical, i.e.…”

Section: A Fully Observed Systemmentioning

confidence: 94%

Section: A Fully Observed Systemmentioning

confidence: 99%

Rate-cost tradeoffs in control

Kostina

Hassibi

2016

2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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show abstract

“…Theorem 2 proves that the converse can be approached by a strikingly simple quantizer coupled with a standard controller, without common randomness (dither) at the encoder and the decoder. Furthermore, although nonuniform rate allocation across time is allowed by Definition 2, such freedom is not needed to achieve (20); the scheme that achieves (20) satisfies H(U i |U i−1 ) → r in the limit of large i.…”

Section: Theorem 2 Consider the Fully Observed Linear Stochasticmentioning

confidence: 99%

Rate-Cost Tradeoffs in Control

Kostina

Hassibi

2019

IEEE Trans. Automat. Contr.

103

158

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Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate r bits/sec and the expected cost b. We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. [2]. The bound applies as long as the differential entropy of the system noise is not −∞. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variablelength vector quantization to prove that the new converse bounds are tight.

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Structural results for two-user interactive communication

Chakravorty

Mahajan

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Optimality of Walrand-Varaiya type policies and approximation results for zero delay coding of Markov sources

Cited by 4 publications

References 28 publications

Rate-cost tradeoffs in control

Rate-cost tradeoffs in control

Rate-Cost Tradeoffs in Control

Structural results for two-user interactive communication

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